Question

The function g(x) = x² + 3px + (14p – 3), where "p" is an integer, has two equal roots.

Find value of "p"

Final answer should be:–
p = 6​

Answer 1

Step-by-step explanation:

Two equal roots means D = 0 of this equation

9p^2 - 56p + 12 = 0

p = [56±√3136-432]/18

p = (56 ± 52)/4

p = 108/4 or 4/4

p = 27 or 1

Please mark my answer as brainliest ❤️

Answer 2

The value of p = 6

Given :

The function g(x) = x² + 3px + (14p – 3) has two equal roots

To find:

Find the value of p

Solution:

Given g(x) has equal roots

As we know if the quadratic equation ax²+bx + c = 0 has equal roots then the discriminant D = 0 here the formula for D is given by

                              D = b²- 4ac  

Now compare given equation x² + 3px + (14p – 3) with ax²+bx + c = 0

⇒ a = 1, b = 3p and c =  (14p – 3)

Since g(x) has equal roots

⇒ b²- 4ac = 0

⇒ (3p)² - 4(1)(14p-3) = 0

⇒  9p² - 56p + 12 = 0

⇒  9p² - 54p -2p + 12 = 0  

⇒ 9p(p-6) - 2(p-6) = 0

⇒ (p-6) (9p-2) =  0

⇒ p-6 = 0      and     9p - 2 = 0

     p = 6                     9p = 2  ⇒   p = 2/9

Given the p is integer

Therefore the value of p = 6

#SPJ2